{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:FRHBA4SY5JT3QJR6KSKX5QYOUT","short_pith_number":"pith:FRHBA4SY","canonical_record":{"source":{"id":"1011.2174","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-11-09T18:59:58Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"388ef9d0469124fa114d1dda662b4e6d8b0643f141995b1d023d876c508aa9d7","abstract_canon_sha256":"e21fb19bdcb845e331b87f22f6b7f27636155d67223d937bbf74750d5676ee06"},"schema_version":"1.0"},"canonical_sha256":"2c4e107258ea67b8263e54957ec30ea4d915c2ff3da1bf1e2d36e466cfebedab","source":{"kind":"arxiv","id":"1011.2174","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2174","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2174v3","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2174","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"pith_short_12","alias_value":"FRHBA4SY5JT3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FRHBA4SY5JT3QJR6","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FRHBA4SY","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:FRHBA4SY5JT3QJR6KSKX5QYOUT","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2174","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-11-09T18:59:58Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"388ef9d0469124fa114d1dda662b4e6d8b0643f141995b1d023d876c508aa9d7","abstract_canon_sha256":"e21fb19bdcb845e331b87f22f6b7f27636155d67223d937bbf74750d5676ee06"},"schema_version":"1.0"},"canonical_sha256":"2c4e107258ea67b8263e54957ec30ea4d915c2ff3da1bf1e2d36e466cfebedab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:31.009195Z","signature_b64":"CN+RhC1uqi5YDCbu+PIrMlmlJ7UklBQ+Rmi8p3Jr48M97nBXN3oFgG5gSt0LvQTdqqYXWjZsJV/vE/u7MD0JAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c4e107258ea67b8263e54957ec30ea4d915c2ff3da1bf1e2d36e466cfebedab","last_reissued_at":"2026-05-18T02:58:31.008455Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:31.008455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2174","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IV8OxUB9ERqQ7BV4mUI201wPfEpFf/CQMpba88jDy1dfkHHQEeVRa1L4XQAtIOnZotrldgne4CuKEmB36V9dBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:18:57.221366Z"},"content_sha256":"f3e0112f6a1b64b901d4426c97af403400102e38b1f552be0d5d3aefe929820d","schema_version":"1.0","event_id":"sha256:f3e0112f6a1b64b901d4426c97af403400102e38b1f552be0d5d3aefe929820d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:FRHBA4SY5JT3QJR6KSKX5QYOUT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extending Structures II: The Quantum Version","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"A.L. Agore, G. Militaru","submitted_at":"2010-11-09T18:59:58Z","abstract_excerpt":"Let A be a Hopf algebra and H a coalgebra. We shall describe and classify up to an isomorphism all Hopf algebras E that factorize through A and H: that is E is a Hopf algebra such that A is a Hopf subalgebra of E, H is a subcoalgebra in E with 1_{E} \\in H and the multiplication map $A\\otimes H \\to E$ is bijective. The tool we use is a new product, we call it the unified product, in the construction of which A and H are connected by three coalgebra maps: two actions and a generalized cocycle. Both the crossed product of an Hopf algebra acting on an algebra and the bicrossed product of two Hopf "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2174","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qFcsJwaBvPiYLdOtNhvpaISITQKRt+83/nimRakPnbZvKl8HYYEyZ9nzZsri3mwu4OUDcUsvMvqbvOZAC1H2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:18:57.221720Z"},"content_sha256":"94645f775cf299a75c868daf6aeefaf75f22c693e1a9829eb0e23802a4cb854f","schema_version":"1.0","event_id":"sha256:94645f775cf299a75c868daf6aeefaf75f22c693e1a9829eb0e23802a4cb854f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FRHBA4SY5JT3QJR6KSKX5QYOUT/bundle.json","state_url":"https://pith.science/pith/FRHBA4SY5JT3QJR6KSKX5QYOUT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FRHBA4SY5JT3QJR6KSKX5QYOUT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T08:18:57Z","links":{"resolver":"https://pith.science/pith/FRHBA4SY5JT3QJR6KSKX5QYOUT","bundle":"https://pith.science/pith/FRHBA4SY5JT3QJR6KSKX5QYOUT/bundle.json","state":"https://pith.science/pith/FRHBA4SY5JT3QJR6KSKX5QYOUT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FRHBA4SY5JT3QJR6KSKX5QYOUT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FRHBA4SY5JT3QJR6KSKX5QYOUT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e21fb19bdcb845e331b87f22f6b7f27636155d67223d937bbf74750d5676ee06","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-11-09T18:59:58Z","title_canon_sha256":"388ef9d0469124fa114d1dda662b4e6d8b0643f141995b1d023d876c508aa9d7"},"schema_version":"1.0","source":{"id":"1011.2174","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2174","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2174v3","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2174","created_at":"2026-05-18T02:58:31Z"},{"alias_kind":"pith_short_12","alias_value":"FRHBA4SY5JT3","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FRHBA4SY5JT3QJR6","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FRHBA4SY","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:94645f775cf299a75c868daf6aeefaf75f22c693e1a9829eb0e23802a4cb854f","target":"graph","created_at":"2026-05-18T02:58:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let A be a Hopf algebra and H a coalgebra. We shall describe and classify up to an isomorphism all Hopf algebras E that factorize through A and H: that is E is a Hopf algebra such that A is a Hopf subalgebra of E, H is a subcoalgebra in E with 1_{E} \\in H and the multiplication map $A\\otimes H \\to E$ is bijective. The tool we use is a new product, we call it the unified product, in the construction of which A and H are connected by three coalgebra maps: two actions and a generalized cocycle. Both the crossed product of an Hopf algebra acting on an algebra and the bicrossed product of two Hopf ","authors_text":"A.L. Agore, G. Militaru","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-11-09T18:59:58Z","title":"Extending Structures II: The Quantum Version"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2174","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f3e0112f6a1b64b901d4426c97af403400102e38b1f552be0d5d3aefe929820d","target":"record","created_at":"2026-05-18T02:58:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e21fb19bdcb845e331b87f22f6b7f27636155d67223d937bbf74750d5676ee06","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-11-09T18:59:58Z","title_canon_sha256":"388ef9d0469124fa114d1dda662b4e6d8b0643f141995b1d023d876c508aa9d7"},"schema_version":"1.0","source":{"id":"1011.2174","kind":"arxiv","version":3}},"canonical_sha256":"2c4e107258ea67b8263e54957ec30ea4d915c2ff3da1bf1e2d36e466cfebedab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c4e107258ea67b8263e54957ec30ea4d915c2ff3da1bf1e2d36e466cfebedab","first_computed_at":"2026-05-18T02:58:31.008455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:31.008455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CN+RhC1uqi5YDCbu+PIrMlmlJ7UklBQ+Rmi8p3Jr48M97nBXN3oFgG5gSt0LvQTdqqYXWjZsJV/vE/u7MD0JAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:31.009195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2174","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3e0112f6a1b64b901d4426c97af403400102e38b1f552be0d5d3aefe929820d","sha256:94645f775cf299a75c868daf6aeefaf75f22c693e1a9829eb0e23802a4cb854f"],"state_sha256":"1fd8831c8465d6ed842195c9e7c4ef5db66cc4fb6c66c2f364753844fe2648cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kene0nc+wHfC/JGY+JG1aMNWushd7PBOCSyv1V/s8wmdazhM7KnZEzfIDYpQVsbB6nsbRVJkBEnvMlYbjIr8Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T08:18:57.223960Z","bundle_sha256":"bbbd9049ad34d41e684f829124146d1c6fcfc618d1bf537d7e96c96a5108c7a7"}}